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<b>let </b><font color="Maroon">c<sub>1</sub></font>, <font color="Maroon">c<sub>2</sub></font> be    <a href="orders_2.html#L1">RelStr</a> ;<br/><b>let </b><font color="Maroon">c<sub>3</sub></font> be   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">c<sub>1</sub></font>;<br/><b>let </b><font color="Maroon">c<sub>4</sub></font> be   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">c<sub>2</sub></font>;<br/>





<a NAME="E1:35"/><i><font color="Green">E17</font></i>: 
the <a href="struct_0.html#U1">carrier</a> of <span class="p1"><a href="yellow_3.html#K3">[:</a><span class="default"><font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span><a href="yellow_3.html#K3">:]</a></span> <a href="hidden.html#R1">=</a> <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default">the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>1</sub></font>,the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>2</sub></font></span><a href="zfmisc_1.html#K2">:]</a></span>
 
<b>by </b><i><a class="ref" href="yellow_3.html#D2">YELLOW_3:def 2</a></i>;<br/>
<div><b>hereby </b> <i><font color="Red">:: according to </font></i><a class="ref" href="tarski.html#D3">TARSKI:def 3</a>,<a class="ref" href="xboole_0.html#D10">XBOOLE_0:def 10</a>
<div class="add"><b>let </b><font color="Maroon">c<sub>5</sub></font> be    <a href="hidden.html#M1">set</a> ;<br/><b>assume </b><a NAME="E1:35_1"/>
<font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="yellow_3.html#K6">[:</a><span class="default"><span class="p2">(<span class="default"><a href="waybel_0.html#K4">uparrow</a> <font color="Maroon">c<sub>3</sub></font></span>)</span>,<span class="p2">(<span class="default"><a href="waybel_0.html#K4">uparrow</a> <font color="Maroon">c<sub>4</sub></font></span>)</span></span><a href="yellow_3.html#K6">:]</a></span>
 ;<br/><b>then consider </b><font color="Maroon">c<sub>6</sub></font>, <font color="Maroon">c<sub>7</sub></font> being    <a href="hidden.html#M1">set</a> <b> such that </b><br/><a NAME="E3:35_1"/><i><font color="Green">E18</font></i>: 
( <font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R2">in</a>  <a href="waybel_0.html#K4">uparrow</a> <font color="Maroon">c<sub>3</sub></font> &amp; <font color="Maroon">c<sub>7</sub></font> <a href="hidden.html#R2">in</a>  <a href="waybel_0.html#K4">uparrow</a> <font color="Maroon">c<sub>4</sub></font> &amp; <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>7</sub></font></span><a href="tarski.html#K4">]</a></span> )
 <b>by </b><i><a class="ref" href="zfmisc_1.html#D2">ZFMISC_1:def 2</a></i>;<br/><b>reconsider </b><font color="Maroon">c<sub>8</sub></font> = <font color="Maroon">c<sub>1</sub></font>, <font color="Maroon">c<sub>9</sub></font> = <font color="Maroon">c<sub>2</sub></font> as  non <a href="struct_0.html#V3">empty</a>  <a href="orders_2.html#L1">RelStr</a>  <b>by </b><i><a class="txt" href="yellow10.html#E3:35_1"><i><font color="Green">E18</font></i></a>, <a class="ref" href="struct_0.html#D1">STRUCT_0:def 1</a></i>;<br/><b>reconsider </b><font color="Maroon">c<sub>10</sub></font> = <font color="Maroon">c<sub>6</sub></font> as   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">c<sub>8</sub></font> <b>by </b><i><a class="txt" href="yellow10.html#E3:35_1"><i><font color="Green">E18</font></i></a></i>;<br/><b>reconsider </b><font color="Maroon">c<sub>11</sub></font> = <font color="Maroon">c<sub>7</sub></font> as   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">c<sub>9</sub></font> <b>by </b><i><a class="txt" href="yellow10.html#E3:35_1"><i><font color="Green">E18</font></i></a></i>;<br/><b>consider </b><font color="Maroon">c<sub>12</sub></font> being   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">c<sub>8</sub></font><b> such that </b><br/><a NAME="E8:35_1"/><i><font color="Green">E19</font></i>: 
( <font color="Maroon">c<sub>12</sub></font> <a href="orders_2.html#R1">&lt;=</a> <font color="Maroon">c<sub>10</sub></font> &amp; <font color="Maroon">c<sub>12</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>3</sub></font> )
 <b>by </b><i><a class="txt" href="yellow10.html#E3:35_1"><i><font color="Green">E18</font></i></a>, <a class="ref" href="waybel_0.html#D16">WAYBEL_0:def 16</a></i>;<br/><b>consider </b><font color="Maroon">c<sub>13</sub></font> being   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">c<sub>9</sub></font><b> such that </b><br/><a NAME="E10:35_1"/><i><font color="Green">E20</font></i>: 
( <font color="Maroon">c<sub>13</sub></font> <a href="orders_2.html#R1">&lt;=</a> <font color="Maroon">c<sub>11</sub></font> &amp; <font color="Maroon">c<sub>13</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>4</sub></font> )
 <b>by </b><i><a class="txt" href="yellow10.html#E3:35_1"><i><font color="Green">E18</font></i></a>, <a class="ref" href="waybel_0.html#D16">WAYBEL_0:def 16</a></i>;<br/><a NAME="E11:35_1"/><i><font color="Green">E21</font></i>: 
<span class="p1"><a href="yellow_3.html#K7">[</a><span class="default"><font color="Maroon">c<sub>12</sub></font>,<font color="Maroon">c<sub>13</sub></font></span><a href="yellow_3.html#K7">]</a></span> <a href="hidden.html#R2">in</a> <span class="p1"><a href="yellow_3.html#K6">[:</a><span class="default"><font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font></span><a href="yellow_3.html#K6">:]</a></span>
 <b>by </b><i><a class="txt" href="yellow10.html#E8:35_1"><i><font color="Green">E19</font></i></a>, <a class="txt" href="yellow10.html#E10:35_1"><i><font color="Green">E20</font></i></a>, <a class="ref" href="zfmisc_1.html#T106">ZFMISC_1:106</a></i>;<br/><a NAME="E12:35_1"/>
<span class="p1"><a href="yellow_3.html#K7">[</a><span class="default"><font color="Maroon">c<sub>12</sub></font>,<font color="Maroon">c<sub>13</sub></font></span><a href="yellow_3.html#K7">]</a></span> <a href="orders_2.html#R1">&lt;=</a> <span class="p1"><a href="yellow_3.html#K7">[</a><span class="default"><font color="Maroon">c<sub>10</sub></font>,<font color="Maroon">c<sub>11</sub></font></span><a href="yellow_3.html#K7">]</a></span>
 <b>by </b><i><a class="txt" href="yellow10.html#E8:35_1"><i><font color="Green">E19</font></i></a>, <a class="txt" href="yellow10.html#E10:35_1"><i><font color="Green">E20</font></i></a>, <a class="ref" href="yellow_3.html#T11">YELLOW_3:11</a></i>;<br/><b>hence </b><a NAME="E13:35_1"/>
<font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R2">in</a>  <a href="waybel_0.html#K4">uparrow</a> <span class="p1"><a href="yellow_3.html#K6">[:</a><span class="default"><font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font></span><a href="yellow_3.html#K6">:]</a></span>
 <b>by </b><i><a class="txt" href="yellow10.html#E3:35_1"><i><font color="Green">E18</font></i></a>, <a class="txt" href="yellow10.html#E11:35_1"><i><font color="Green">E21</font></i></a>, <a class="ref" href="waybel_0.html#D16">WAYBEL_0:def 16</a></i>;<br/></div>
<b>end;</b></div>

<b>let </b><font color="Maroon">c<sub>5</sub></font> be    <a href="hidden.html#M1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="tarski.html#D3">TARSKI:def 3</a><br/>

<b>assume </b><a NAME="E3:35"/><i><font color="Green">E18</font></i>: 
<font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R2">in</a>  <a href="waybel_0.html#K4">uparrow</a> <span class="p1"><a href="yellow_3.html#K6">[:</a><span class="default"><font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font></span><a href="yellow_3.html#K6">:]</a></span>
 ;<br/>

<b>then consider </b><font color="Maroon">c<sub>6</sub></font>, <font color="Maroon">c<sub>7</sub></font> being    <a href="hidden.html#M1">set</a> <b> such that </b><br/><a NAME="E5:35"/><i><font color="Green">E19</font></i>: 
( <font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R2">in</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>1</sub></font> &amp; <font color="Maroon">c<sub>7</sub></font> <a href="hidden.html#R2">in</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>2</sub></font> )
 <b>and </b><br/><a NAME="E6:35"/>
<font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>7</sub></font></span><a href="tarski.html#K4">]</a></span>
 <b>by </b><i><a class="txt" href="yellow10.html#E1:35"><i><font color="Green">E17</font></i></a>, <a class="ref" href="zfmisc_1.html#D2">ZFMISC_1:def 2</a></i>;<br/>
<b>reconsider </b><font color="Maroon">c<sub>8</sub></font> = <font color="Maroon">c<sub>1</sub></font>, <font color="Maroon">c<sub>9</sub></font> = <font color="Maroon">c<sub>2</sub></font> as  non <a href="struct_0.html#V3">empty</a>  <a href="orders_2.html#L1">RelStr</a>  <b>by </b><i><a class="txt" href="yellow10.html#E5:35"><i><font color="Green">E19</font></i></a>, <a class="ref" href="struct_0.html#D1">STRUCT_0:def 1</a></i>;<br/>
<b>reconsider </b><font color="Maroon">c<sub>10</sub></font> = <font color="Maroon">c<sub>5</sub></font> as   <a href="struct_0.html#NM1">Element</a> of <span class="p1"><a href="yellow_3.html#K3">[:</a><span class="default"><font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>9</sub></font></span><a href="yellow_3.html#K3">:]</a></span> <b>by </b><i><a class="txt" href="yellow10.html#E3:35"><i><font color="Green">E18</font></i></a></i>;<br/>
<b>consider </b><font color="Maroon">c<sub>11</sub></font> being   <a href="struct_0.html#NM1">Element</a> of <span class="p1"><a href="yellow_3.html#K3">[:</a><span class="default"><font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>9</sub></font></span><a href="yellow_3.html#K3">:]</a></span><b> such that </b><br/><a NAME="E10:35"/><i><font color="Green">E20</font></i>: 
( <font color="Maroon">c<sub>11</sub></font> <a href="orders_2.html#R1">&lt;=</a> <font color="Maroon">c<sub>10</sub></font> &amp; <font color="Maroon">c<sub>11</sub></font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="yellow_3.html#K6">[:</a><span class="default"><font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font></span><a href="yellow_3.html#K6">:]</a></span> )
 <b>by </b><i><a class="txt" href="yellow10.html#E3:35"><i><font color="Green">E18</font></i></a>, <a class="ref" href="waybel_0.html#D16">WAYBEL_0:def 16</a></i>;<br/>
<a NAME="E11:35"/><i><font color="Green">E21</font></i>: 
( <font color="Maroon">c<sub>11</sub></font> <a href="yellow_3.html#K8">`1</a>  <a href="orders_2.html#R1">&lt;=</a> <font color="Maroon">c<sub>10</sub></font> <a href="yellow_3.html#K8">`1</a>  &amp; <font color="Maroon">c<sub>11</sub></font> <a href="yellow_3.html#K9">`2</a>  <a href="orders_2.html#R1">&lt;=</a> <font color="Maroon">c<sub>10</sub></font> <a href="yellow_3.html#K9">`2</a>  )
 
<b>by </b><i><a class="txt" href="yellow10.html#E10:35"><i><font color="Green">E20</font></i></a>, <a class="ref" href="yellow_3.html#T12">YELLOW_3:12</a></i>;<br/>
<a NAME="E12:35"/>
( <font color="Maroon">c<sub>11</sub></font> <a href="yellow_3.html#K8">`1</a>  <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>3</sub></font> &amp; <font color="Maroon">c<sub>11</sub></font> <a href="yellow_3.html#K9">`2</a>  <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>4</sub></font> )
 
<b>by </b><i><a class="txt" href="yellow10.html#E10:35"><i><font color="Green">E20</font></i></a>, <a class="ref" href="mcart_1.html#T10">MCART_1:10</a></i>;<br/>
<a NAME="E13:35"/><b>then </b><i><font color="Green">E22</font></i>: 
( <font color="Maroon">c<sub>5</sub></font> <a href="mcart_1.html#K1">`1</a>  <a href="hidden.html#R2">in</a>  <a href="waybel_0.html#K4">uparrow</a> <font color="Maroon">c<sub>3</sub></font> &amp; <font color="Maroon">c<sub>5</sub></font> <a href="mcart_1.html#K2">`2</a>  <a href="hidden.html#R2">in</a>  <a href="waybel_0.html#K4">uparrow</a> <font color="Maroon">c<sub>4</sub></font> )
 
<b>by </b><i><a class="txt" href="yellow10.html#E11:35"><i><font color="Green">E21</font></i></a>, <a class="ref" href="waybel_0.html#D16">WAYBEL_0:def 16</a></i>;<br/>
<a NAME="E14:35"/>
<font color="Maroon">c<sub>10</sub></font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="yellow_3.html#K7">[</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="yellow_3.html#K8">`1</a> </span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="yellow_3.html#K9">`2</a> </span>)</span></span><a href="yellow_3.html#K7">]</a></span>
 
<b>by </b><i><a class="txt" href="yellow10.html#E1:35"><i><font color="Green">E17</font></i></a>, <a class="ref" href="mcart_1.html#T23">MCART_1:23</a></i>;<br/>
<b>hence </b><a NAME="E15:35"/>
<font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="yellow_3.html#K6">[:</a><span class="default"><span class="p2">(<span class="default"><a href="waybel_0.html#K4">uparrow</a> <font color="Maroon">c<sub>3</sub></font></span>)</span>,<span class="p2">(<span class="default"><a href="waybel_0.html#K4">uparrow</a> <font color="Maroon">c<sub>4</sub></font></span>)</span></span><a href="yellow_3.html#K6">:]</a></span>
 <b>by </b><i><a class="txt" href="yellow10.html#E13:35"><i><font color="Green">E22</font></i></a>, <a class="ref" href="mcart_1.html#T11">MCART_1:11</a></i>;<br/>


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